Answer to Question #217933 in Statistics and Probability for Vickie

Question

A farmer wants to test whether the average yield for three farms is the same, samples of yields over a period of five years were taken from each of the farms the computations have been made

Between sum squares 70

Within sum of squares 122

1)find the null and alternative hypothesis

2) compute the value of f and determine whether is a difference in the yields of the three farms

Answer 1

1) $H_0:\mu_1=\mu_2=\mu_3.$

$H_a:$ not all $\mu_i$ are equal.

2) $SS_B=70,\;SS_W=122.$

$df_B=3-1=2,\;df_W=5*3-3=12.$

$MS_B=\frac{70}{2}=35,\; MS_W=\frac{122}{12}=10.17.$

$F=\frac{35}{10.17}=3.44.$

P-value: $p=0.0659.$

Since the p-value is greater than 0.05, fail to reject the null hypothesis.

The difference in the yields of the three farms is not significant.